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Original citation: Ma, L. and Staunton, R. C. (2012). Analysis of the contour structural irregularity of skin lesions using wavelet decomposition. Pattern Recognition, 46(1) Permanent WRAP url: http://wrap.warwick.ac.uk/49978 Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes the work of researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available. Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher’s statement: “NOTICE: this is the author’s version of a work that was accepted for publication in Pattern Recognition. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Pattern Recognition, [VOL:46, ISSUE:1, January 2013)] DOI:10.1016/j.patcog.2012.07.001” A note on versions: The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher’s version. Please see the ‘permanent WRAP url’ above for details on accessing the published version and note that access may require a subscription. For more information, please contact the WRAP Team at: wrap@warwick.ac.uk

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PRE-PRINT Accepted version, before formatting and proof reading. Final article is in Pattern Recognition 46 (2013) 98–106

Analysis of the contour structural irregularity of skin lesions

using wavelet decomposition

Li Ma1 and Richard C. Staunton2

1College of Life Information Science & Instrument Engineering, Hangzhou Dianzi University, 310018, China. Email: mali@hdu.edu.cn 2School of Engineering, University of Warwick, Coventry CV4 7AL, U. K. Email: r.c.staunton@warwick.ac.uk Corresponding author: R.C. Staunton. Phone: +44 2476 523980, Fax: +44 2476 418922 Abstract The boundary irregularity of skin lesions is of clinical significance for the early detection of malignant melanomas and to distinguish them from other lesions such as benign moles. The structural components of the contour are of particular importance. To extract the structure from the contour, wavelet decomposition was used as these components tend to locate in the lower frequency sub-bands. Lesion contours were modeled as signatures with scale normalization to give position and frequency resolution invariance. Energy distributions among different wavelet sub-bands were then analyzed to extract those with significant levels and differences to enable maximum discrimination. Based on the coefficients in the significant sub-bands, structural components from the original contours were modeled, and a set of statistical and geometric irregularity descriptors researched that were applied at each of the significant sub-bands. The effectiveness of the descriptors was measured using the Hausdorff distance between sets of data from melanoma and mole contours. The best descriptor outputs were input to a back projection neural network to construct a combined classifier system. Experimental results showed that thirteen features from four sub-bands produced the best discrimination between sets of melanomas and moles, and that a small training set of nine melanomas and nine moles was optimum. Keywords: melanoma detection, structural irregularity of contours, wavelet decomposition, multi-scale descriptors, significant wavelet sub-bands

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1. Introduction Melanomas are malignant tumors comprised of epidermal or mucosal cells and have a high possibility of lymphatic metastasis resulting in unfavorable prognosis. Early detection of melanomas in clinics depends on a well-known ABCD rule to determine the benign or malignant nature of skin lesions [1]. That is, Asymmetry of the lesion’s boundaries, Boundary irregularity, Color distributions and lesion Diameters. Alternative classifications based on color texture appearance has been researched recently [2, 3], and by employing a biopsy and electron tomography, a classification from 3D cell images has been reported [4]. The technique of dermoscopy used polarized light or oil coverage to make more of a lesion’s structure visible [5]. CAD systems have been researched to aide the clinician. These often comprise image acquisition, artifact detection, lesion segmentation, feature extraction and lesion classification stages [6]. In the previous decade, there have been many studies concerning the boundary irregularity of lesions using both geometric [7,8,9,10] and local fractal [11] measures. There are two types of irregularities found on boundaries: textual and structural, these correspond to fine changes and obvious convex and concave features respectively [7]. The structural irregularity has clinical importance for melanoma diagnosis. The first task of boundary irregularity analysis is to identify and extract the boundary as a 1D signal from the 2D image. The contours of skin lesions can be considered as a mixture of structural and textural irregularity as can be seen by following those in Fig.1. The benign mole is smooth with little variation on its contour, while that of the melanoma contains many indents and protrusions in its structure, and has an obvious visual roughness. However, for measurements of structural irregularity, multi-scale analysis of skin lesion boundaries is an important technique for correctly isolating the structural from the textural information. Wavelet transforms are useful multi-resolution analytical tools for revealing object information at a defined scale or to select particular frequency bands of interest [12]. A requirement for the design of structural irregularity descriptions is to explore ways of extracting features not only from structural variations along the original contour, but also to separate the scaled information in the significant sub-bands and thus with this extra information to improve the accuracy of the diagnosis. Previously T. K. Lee proposed an irregularity measure based on a deduced scale level using a curvature model of multi-scaled boundaries [7]. However it involved heavy computation as the proposed irregularity index was evaluated from a hierarchical structure with its roots as global curve segments and leaves as local segments for each of the consecutive smoothed contours. The Gaussian smoothing-scale increases on the original lesion contour indicated the evolution of the curve’s indented and protruding segments. The motivation for this study is to show that the filtered information in the sub-bands can be used by structural irregularity descriptors to provide a good separation between melanomas and benign moles. We show that multi-scale wavelet decomposition of the extracted contour

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followed by the selection of significant sub-bands can be an appropriate approach for the evaluation of structural irregularity. The novelty of the proposed structural irregularity features is:- (1) The extracted structural components of the contours are reconstructed by the summation of the approximate wavelet coefficients at the selected maximum scale and only those detail coefficients that are from structurally significant sub-bands; (2) Two classes of statistical and geometric irregularity descriptors are defined and used. These were evaluated in each of the significant sub-band to determine firstly that they were independent and did not correlate with other features, and secondly their effectiveness in distinguishing between melanomas and moles was measured. Features were discarded if they did not separate sets of moles and melanomas sufficiently in order to maintain a compact feature space. The steps in the procedure to reconstruct just the structural components of the contours are:- Perform a 1D wavelet decomposition to produce a series of detailed contour signals for all the lesion contours in the data set; Calculate energy measures for each of the detail, that is high frequency, sub-bands; Perform a Hausdorff Distance (HD) [13,14] analysis based on energy values in each sub-band to determine which detail coefficients are significant for distinguishing the two sets; Select the significant sub-bands; Label the sub-bands with scales below these as containing the textural component of the contour and rejected them from further consideration; Sum the approximation coefficients and the remaining detail coefficients to generate the connected structural component of the contour. This procedure approximately isolates the structural portion of the original contour, and then the irregularity descriptors are used to refine this and partition the lesions appropriately.

(a) (b) Fig.1 Images of skin lesions (a) mole (b) melanoma

Section 2 describes the procedure to extract the structural components of the lesion contours including the wavelet decomposition, the scale normalization necessary to process contours of different length, and the selection of the significant sub-bands. Section 3 discusses the design of the statistical and geometric descriptors of contour irregularity that are applied at multi-scales. Section 4 concerns the selection techniques that ensure features are independent and that the

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feature vector is compact. Section 5 provides the experimental results for the significant structural component extraction and feature evaluation. A combined classifier using a back projection neural network is described together with issues concerning training and the evaluation of the structure of the feature vector. Finally Section 6 provides conclusions. 2. Extraction of the structural components of the skin lesion contours 2.1 Wavelet decomposition of a lesion contour The contour of a skin lesion in an image is described by the points. C=x1,y1,x2,y2,…,xN,yN. There are two ways of to represent this 2D data as a 1D signal: 1) The contour is split into two 1D sub-vectors Cx=x1,x2,…,xN and Cy=y1,y2,…,yN; or 2) The contour is modeled as a signature Cr=r1,r2,…,rN where the radial distance from the geometric center,

2'2' )()( yyxxr iii −+−= , i=1,2,…n and (x',y') is the coordinate of the geometric center of

the closed contour. The signature representation was adopted in the paper as it provided the advantage of position invariance. 2.1.1 Scale normalization It was noted that many moles have a shorter contour for a given nominal area than do melanomas. Together with size variability between the samples in the database, this can lead to variations in estimated frequency and resolution in the frequency domain. Scale normalization is required to enable a comparison between moles and melanomas in this domain. The proposed normalization was modified from [15] to give radius:

<+

=′

otherwiseNnir

TirNnir

ri

)(

)(-)( 21 µµ i=1,2,…,N (1)

Where i is an integer used to resample the contour points with a spacing distance of (n/N) and

the ceiling function is used to produce an integer index to r. The values µ1 and µ2 are the

averaged radial distances of all the melanomas and benign moles respectively in the data base. Their inclusion provides a mean value platform on to which the lowest level approximation coefficients will be superimposed. T is a threshold used to determine if a mole has a small value of r. If so, r is increased to reach a similar size to that of a melanoma. For melanomas and large

moles, the value of r is never increased. ir′ is the radial distance of the ith point of a contour

after this normalization. The lesions were sometimes small with r(i) < T, and sometimes not circular with sections where r(i) < T. In these cases normalizing the individual r(i) was performed to improve the discrimination of the classifiers described in the later sections.

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2.1.2 Wavelet decomposition Wavelet decomposition is a powerful tool for multi-scale signal analysis. By using a pair of low-pass and high-pass filters, an original signal is decomposed into approximation and detail coefficients with the approximations feeding into the next level of decomposition, and thus creating a decomposition tree [16]. The tree structure of such a 1D wavelet decomposition is shown in fig 2.

Fig.2 Tree structure of wavelet decomposition A 1D wavelet decomposition is performed on a contour signature Cr. The approximate and

detail coefficients at scale i are given by iM

iii aaaA ,, 21= and iM

iii dddD ,, 21=

respectively where M = N / 2i. As the scale increases, the approximate coefficients are further decomposed into low and high frequency components at the next higher scale. Generally the textural components of a contour occupy the lower scale, higher frequency bands, with the energy distributed evenly between bands to give a relatively small total energy within each. However the structural components generally have a larger energy and occupy the lower frequency bands. By using wavelet decomposition to level s, an original contour signature Cr is

transformed to a series of sub-band signals 11,,, DDDA sss − covering the whole signal

frequency space at ],2/1,0[ maxfs ]2/1,2/1[ max1

max ff ii − , 1,2,,1, −= ssi and fmax is half

the sampling frequency. This represents a concatenation of the frequency bands from the lowest to the highest. The task is to identify at which decomposition levels the structural components of a lesion contour can be extracted and which sub-bands in the frequency domain are significant for distinguishing moles and melanomas.

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2.2 Sub-band descriptions of contour structural components For a 1D contour signal, the FFT provides the magnitude and phase against frequency. The weakness of the FFT is that the spectral profiles are unrelated to the position of an event in the boundary and the resolution is fixed throughout the frequency band. On the other hand the discrete wavelet transform (DWT) presents the capability of confining signal components to dyadically increasing width frequency bands with different resolutions. The left two columns of Fig.3 present mole, and the right two melanoma data. The plot in the first row of the first column is the FFT spectrum of a mole where the zero frequency component has been translated to the center. The plot on the right indicates the sub-band division in the frequency domain when two levels of wavelet decomposition are implemented. A1, A2, D1, D2, refer to approximate and detail signals. The plots in the rows below show the signals in each band. Similarly the two columns on the right are for a melanoma. Differences can be seen between the mole and the melanoma signals in the D1 and D2 bands. We continue to describe the selection of the bands which enable the best discrimination between moles and melanomas.

Fig.3 Spectral and wavelet comparisons between a mole and a melanoma. Mole: (a) FFT, (b) A1, A2, D1, D2 wavelet coefficient frequency map, (c) A1, (d) D1, (e) A2, (f) D2; Melanoma: (g) FFT, (h) A1, A2, D1, D2 wavelet coefficient frequency map, (i) A1, (j) D1, (k) A2, (l) D2; 2.2.1 Significant sub-band selection To obtain just the contour’s structural components, several lower frequency sub-bands need to be identified from which to reconstruct that portion of the original contour using both multi-scale approximate and detail coefficients. The evaluation of the significant sub-band range was performed between each of the sample sets by HD distribution analysis at each level of wavelet decomposition [17]. When analyzing the decomposition of a contour signal, the total energy at any decomposition level indicates the significance of that sub-band frequency to the original signal. The energy of a wavelet sub-band Dj is defined as

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2)(∑=i

jij DE j=1,2,…n (2)

2.2.2 Procedure for investigating significant sub-band selection An algorithm was developed to identify those sub-bands which enabled the largest discrimination between moles and melanomas. Given a set of p benign mole contours,

,,, 21bp

bbb xxx =Ω where bkx was the kth contour, and a set of q melanoma contours,

,,, 21mq

mmm xxx =Ω where mkx was the kth contour.

Step1. For a preset maximum level of wavelet decomposition n, calculate the wavelet energy for

every contour bkx and m

kx within each set Ωb and Ωm. First perform wavelet decomposition to

obtain the detail sub-band signals, Dn, Dn-1, … D1, for each lesion contour, and then calculate the

energy for either bkx or m

kx in each band, blkE and m

lkE , where sub-band nl ,,2,1 =

using Eq.(2).

Step2. Form energy sets ,,E 21b b

lpbl

bl EEE ，= and ,,E 21

m mlq

ml

ml EEE ，= from the

individual energies calculated for each transformed benign and melanoma contour at each

sub-band nl ,,2,1 = .

Step3. Compute the lHD value between energy sets of moles bE and melanomas mE for

each band nll ,,2,1, = . This measures the discrimination between the two classes for each

sub-band.

Step4. Plot the distribution of lHD with respect to sub-band number l . The sub-bands with

the highest HD are considered as the most significant and used in the final classification. Step5. The sub-bands with the higher HDs are considered as significant bands for use in classification. 2.2.3 Extraction of the structural component of a lesion contour Based on the theory of wavelet reconstruction, the structural component of a lesion contour is

given by combining the significant coefficient groups from 11,,, DDDA sss − where the

original decomposition was stopped at level s. The decomposed detail sub-bands need to be divided into high-scale (low-frequency) and low-scale (high-frequency) groups using a

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threshold st so that:

tsssss DDDAC ++++= − 1 (3)

121 DDDC tt sst +++= −− (4)

Where Cs contains lower-frequency information and represents the structural component of the contour, and Ct contains higher-frequency information and represents the textural component. Choosing both s and st are difficult tasks, as a large s generates many narrow sub-bands close to zero frequency. Although these will contain structural information that will be relatively free of textural irregularity, there is an extra cost in increased computational complexity. A small s can lead to structural contours contaminated with textural irregularity. The value of st chosen is crucial to obtain useful structural and textural contour information. The significant sub-band selection process described in Section 2.2.2 was run on the test data and in practice the HD distribution (Fig. 4) produced had a single peak that lead to the straightforward selection of a single, general value for st as described in Section 5.1.

3. Descriptors of contour irregularity at multiple scales Irregularity measures of object boundaries are key components for shape related classifications. They are used after the contour structural components have been extracted. There are two categories of irregularity descriptors, with one based on statistical measures, and the other on geometry. The descriptors are only extracted at the previously determined significant levels

Ω∈jj, , where Ω is a significant level set formed by the sub-band selection procedure of

Section 2.2.2. 3.1 Statistical measures Together with the mean and variance of the energy of Dj at each significant level [9], the following features related to contour irregularity were defined:-

1) Entropy of wavelet energy, ( )ji

N

i

jij ppw log

1∑=

−= (5)

where jji

ji EEp = is the energy probability of the ith component of Dj , Ej is the total energy

of the coefficients in band j as calculated by eqn (2), and 2j

ij

i DE = . The energy entropy

measures the magnitude of signal fluctuations.

2) Ultimate width. For any signal NxxxX ,..., 21= , the ultimate width is defined as

µσ×

=2width (6)

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Where µ and σ are the mean and variance of signal X. A large width indicates sharp variations. 3.2 Geometric based irregularity measures At each significant level j, a supposed structural component Cj, s ≥ j ≥ st of a contour is reconstructed from the wavelet coefficients, Cj = As + Ds + Ds-1 + … + Dj. In addition to a simple variance measure [11], the other irregularity measures of the reconstructed contours are evaluated as:-

Radial Deviation, |)(|1

1∑=

−=N

ii rr

NRD (7)

where r is the mean radius of the contour signature.

Contour Roughness [8], ∑ −==

+N

iii rr

NRo

11 ||1

(8)

Irregularity Measure, )(

)(

s

sjSArea

SCAreaIM

⊕= (9)

where Ss is reconstructed from the approximate data, As, at the significant level s, and ⊕ is the exclusive-or operator. 4. Feature selection Feature selection was performed to remove some measures that were too similar to others and to identify those that were most independent for inclusion in an efficient feature vector. Initially 25 features were identified from six irregularity descriptors at four scales plus IM at the threshold scale st. Then a correlation analysis followed by a performance based feature selection was performed as detailed below. 4.1 Correlation analysis Correlation analysis is a popular tool for removing those redundant features that have a strong

relationship to others within a feature vector [18]. Given a feature vector ntttF ,,, 21 and a

sample set mxxxS ,,, 21 = , the correlation coefficient ρij of any pair of features ti,tj is

calculated as follows:

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( )( )

( ) ( )∑∑

∑

==

=

−−

−−

=m

pjpj

m

pipi

m

pipjipi

ij

ztzt

ztzt

1

2

1

2

1ρ (10)

where zi is the mean value of feature ti in the sample set and tpi is the value of ti for the sample xp. The absolute value of ρij indicates the correlation between ti and tj, so a redundant feature will have a large ρij. The following is the procedure for removing redundant features using correlation analysis:- Step 1. Given an original feature vector F and a sample set S, Calculate a matrix of correlation

coefficients, njijiij ≤≤≠ ,1,,ρ using Eq.(10). ;

Step 2. Given a preset threshold T, split the pairs of features (ti,tj ), where (i ≠ j, 1 ≤ i, j ≤ n), into

two sets, where njijiTFF ij ≤≤≠<= ,1,,|1 ρ is a set that does not contain redundant

features in F, and |),,2 TjiptF ijp ≥∈= ρ is generated by choosing either feature of a

highly correlated pair. Selection can equally be random, or we kept the one that computed most efficiently.

Step 3 The final feature set after removing redundant components is given by 21 FFF ∪=′ .

4.2 Performance based feature selection After removing the redundant features from the vector, those remaining are largely independent. Further analysis is then performed to select the best features based on their discrimination performance. To evaluate the discrimination, the contribution to the correct classification for each feature is evaluated [7]. Given a sample set of skin lesions with manually labeled classes w1 and w2, representing benign moles and malignant melanomas respectively, the probability

distributions ( )2| wtP i , and ( )1| wtP i are evaluated for each feature. Suppose the prior

probabilities p(w1) and p(w2) are equal, then the posterior probabilities ( )itwp |1 and

( )itwp |2 will be closely related to ( )1| wtp i and ( )2| wtp i . The classification is perfectly

separable when any value of ( ) 0| 2 ≠wtp has the corresponding value of ( ) 0| 1 =wtp , and

is absolutely inseparable when ( ) ( )12 || wtpwtp = at any point [19].

However, medically, the probability of a benign mole p(w1) is larger than that of a melanoma p(w2). With the Bayesian rule, the discrimination can be stated: If

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)()|()()|( 2211 wpwxpwpwxp > , then 1wx∈ . Here this is simplified to be

)|()|( 21 wxpwxp > using )()( 21 wpwp = . This proposed simplification is justified when

)|( 1wxp is located to the left side of )|( 2wxp . This is true as the features, measuring contour

roughness, take smaller values in moles than that in melanomas. In addition, our rule has the same averaged error probability as the Bayesian, because if

)|()|( 21 wxpwxp > , )()( 21 wpwp > , then

)()|()()|()()|( 221211 wpwxpwpwxpwpwxp >> ⇒ )()|()()|( 2211 wpwxpwpwxp >

Generally conditional probabilities of the feature ti for two classes will be overlapped. The degree of overlapping of the two probability distributions was used as a measure of classification error for any single feature ti.

Suppose ,,, 21 rtttF =′ was the feature vector after redundancy removal. The steps used

for performance based feature selection were:-

Step 1: Conditional probability distributions. For each feature Fti ′∈ , calculate the

conditional probability distributions )|( 1wtp i and )|( 2wtp i for benign and malignant

lesions in the sample sets; Step 2: Accumulated probabilities. Given a threshold T, find an appropriate value of k to

compute the accumulated probabilities TpP kj

bj

ib ≥∑= =1 and ∑= +=

Nkj

mj

im pP 1 for each

feature it . Where bjp and m

jp are the jth values of )|( 1wtp i and )|( 2wtp i .

Step 3: Feature verification. For each feature Fti ′∈ ( pi ≤≤1 ), If ibP ≥ T and i

mP ≥ T,

the feature ti is verified with a classification error of less than 1-T, otherwise ti is discarded. Where T is a preset value that is chosen to be large enough to secure a sufficient classification

accuracy. The final feature set is then ,,, **2

*1

*qtttF = , Fti ′∈* ( pqqi ≤≤≤ ,1 ).

5. Experimental results Three experiments were performed:- Significant wavelet sub-band selection; Reconstruction of skin lesion contour from wavelet decompositions; And an evaluation of the proposed multi-scale descriptors of contour irregularity using a combined classifier based on a back projection neural network

The test data comprised 134 images of skin lesions, with 72 melanomas and 62 moles.

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They were downloaded from the Dermnet Skin Disease Image Atlas database at http://www.dermnet.com/. The images were randomly selected from the database, after viewing to remove some images that contained defocussed patches. Most images were of size 120x120 pixels, and if not, they were converted to this size by resampling. Each was converted from color to gray level before processing. For the purpose of classification, a training set was formed by randomly selecting 31 moles and 36 melanomas from the sample set, with the remaining samples being used as test samples. The experiments were implemented using MATLAB 7.6. 5.1 Significant level selection and reconstruction of the structural component of a contour Based on the procedure for significant sub-band selection described in Section 2.2.2, the significant levels were identified using the training set and the ‘db3’wavelet. The maximum level of decomposition was preset to 10. Then the HD between the averaged sub-band energies of the wavelet detail coefficients for each class was measured at each level. The distribution is shown in Fig.4 where it can be seen that levels 1 to 5 have a low flat distribution, levels 6 to 9 have a monotonically increasing HD, and that the HD at level 10 has decreased again. The coefficients in levels D1 to D5 cover the higher frequencies where there are similar small textural variations for both moles and melanomas. The detail coefficients in D10 locate at the low frequencies where there is some basic structure, but for computational efficiency it was found to be better to use this when included in the approximation set A9. Therefore, as expected, with HDs up to 3.1, the middle-frequency bands represented by D6 to D9 have been shown to contain significant discrimination information, and these were selected as the significant levels.

Fig.4 HD distribution of wavelet detail signals v. level

It is simple to reconstruct the structural components of the contour after the significant levels in the wavelet decomposition stack have been determined. Fig.5 shows the extracted contours of a mole (a,b,c) and a melanoma (d,e,f), where Fig.5 a) and d) are the original contours. Fig.5 b)

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and e) are the corresponding contours reconstructed from A9 and D1 to D5. The approximation coefficient, A9 has been included to give the basic structure of the contour onto which the more complex textural part has been superimposed. Fig.5 c) and f) are reconstructed from A9 and D6 to D9 (s = 9, st = 6), that is the boundaries representing the structural portion of the original lesion. With the textural information removed, these have the property of the highest discrimination between different lesion classes. In the remainder of the paper these significant sub-bands will be referred to as the structural sub-bands.

Fig.5 Contours after wavelet reconstruction. (a) Mole - original, (b) Mole - textural, (c) Mole – structural, (d) Melanoma – original, (e) Melanoma – textural, (f) Melanoma – structural. (Angle in degrees and Radius in pixels, with inner dotted circle at 100 and solid circle at 200).

5.2 Results of feature selection As described in Section 4, the original feature vector consisted of 25 irregularity features that were formed from seven measures, six of which were applied at each of four significant sub-bands. At the first stage of feature selection, correlation analysis, nine of these features were removed to decrease redundancy. Table 1 shows the retained (tick) and removed (cross) features. The average energy, wavelet entropy and ultimate width were reliable features at most levels of the significant sub-bands. The other independent features retained included the variance at the two higher levels (8 and 9), the radial deviation at level 6, the contour roughness at level 7, and the irregularity measure at level 6.

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Wavelet Level

Averaged energy

Wavelet entropy

Ultimate width

Variance Radial deviation

Contour roughness

Irregularity measure

6 √ √ √ x √ x √ 7 √ √ √ x x √ 8 √ √ x √ x x 9 √ √ √ √ x x

Table 1. Results of feature selection after correlation analysis After removal of the redundant features identified by the correlation analysis, selection was taken further for the remaining 16 features by a classification performance analysis of each feature. As discussed in Section 4.2, the cumulative probability distribution of each feature was

calculated for both the benign, ∑==

k

i

bib pP

1, and the melanomas, ∑=

+=

N

ki

mim pP

1, in the sample

sets, where N was the largest observed value for that feature and k was a value satisfying

TpPk

i

bib ≥=∑

=1

. A threshold T = 0.75 was chosen experimentally that indicated correct

classification for every feature when applied to the benign samples in the training set. Then the feature had to meet the requirement Pm > T to be retained within the overall feature vector. Fig.6 presents the results of the final feature selection.

Fig.6 Plot of accumulated probabilities:- (a) Pb ; (b) Pm, for each of the 16 features

In Fig 6 it can be confirmed that all the features had a value of Pb larger than threshold T = 0.75 and there were three features with Pm values that were less than T. They were the averaged energy at level 9, and variances at level 8 and 9. These were discarded, leaving 13 features for

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further classification. It was noticed that some Pm values approached 1.0, signifying there was little overlap between the probability distributions of the benign and melanoma sets for these features. 5.3 Combined classification results The results of selections and tests on the individual features have been presented in Sections 5.1 and 5.2. In this section a Back Projection (BP) neural network is described that was used to perform classification of skin lesions based on a combination of the 13 selected features. The neural network had a structure of three layers:- input layer with 13 nodes; hidden layer with 3 nodes; and output with one node [20]. The training parameters were a preset training error of 0.01 and a maximum training number of 1000 iterations. As before, the main training set was formed by randomly selecting 31 moles and 36 melanomas from the sample set, with the remaining samples forming the testing set. A sub-set of the large training set was randomly formed to produce an alternative small training set of 9 moles and 9 melanomas. To study the discrimination ability of the proposed multi-scale based feature vector and to refine its operation, some classification experiments were performed to compare firstly single-scale with multi-scale features, and then multi-scale feature either before feature selection (25 features), or after (13 features). This was performed with both the small and large sized training sets to see which gave the best results.

5.3.1 Before feature selection Four experimental schemes were tried for training the BP network:- (1) Multi-scale, with all 25

features and the small training set; (2) Single scale, with 7 features at level 9 and the small training

set; (3) Multi-scale features and the large training set; and (4) Single scale features and the large

training set. After each training and processing of the test data, their corresponding Receiver

Operating Characteristic (ROC) plots were generated and are shown in Fig.7.

The input layer of the neural network has m values, where m is the number of features calculated

from each sample in the test data set. The output of the network produces a single real value between

0 and 1 to indicate which class the sample belongs to for each of the S samples in the test data set.

Overall the network produces an output vector with dimension S. Given a threshold value between 0

and 1, the output vector is converted to a binary vector with elements 0 and 1 indicating the class

estimations. Each sample in the set has previously been classified by a clinician and so the TP and

FP values for this threshold can be calculated. This process is repeated for a range of thresholds

between 0 and 1 and the resulting FP,TP pairs plotted as an ROC curve that spans from the bottom

left (1,0) to the top right corner (0,1).

The nearer the ROC trace is to the top left corner, the better the discrimination of a scheme [21,22,23]. Fig.7 shows that the worst plot, is the single scale with a small training set, and the best, that clearly locates towards the top left corner, was for the multi-scale features using the

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small training set. This had a better classification power than the multi-scale scheme using the large training set. The multi-scale features were always found to perform better than the single scale features. In addition, the multi-scale features provided a way of improving the discrimination when only a small sized training set was available.

Fig.7 ROC plots of the different training schemes before feature selection.

5.3.2 After feature selection In this section the classification performances of the features selected by the different schemes have been compared. Feature selection has only been reported for the multi-scale case as the results of Section 5.3.1 have already confirmed multi-scale processing to be superior. The following experiments were designed to compare the multi-scale features before and after selection using both the large and small training sets. In order to reach a generality for the small training set, an averaged ROC plot has been generated from 15 randomly selected possible small training sets of 9 moles and 9 melanomas. In effect this was achieved by providing 15 parallel neural networks, averaging their real valued outputs, converting this to binary at each threshold value from 0 to 1 and then plotting the TP, FP rates accumulated from all the test samples on the ROC. The number of combination of all possible sets was too big to test

at ( )931

936 CC × .

The ROC in Fig.8 gives a comparison of results when features are used at multiple-scales.

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Results are with and without feature selection, and for large and small training image sets. From Fig.8 the best classification performance is for 13 selected multi-scale features with a small training set. It should be noted that this ROC plot has resulted from the averaged outputs of the 15 separately trained neural network classifiers using the test set. The next best is for the 13 selected multi-scale features with a large training set, followed by the 25 original multi-scale features using the large training set, and finally the 25 original multi-scale features using the small training set.

Fig.8 ROC plots for feature selection using multi-scale features

5.3.3 Design of parallel classifiers using small training sets The results in Fig 8 have indicated that the averaged output of 15 neural classifiers using small training sets can outperform a single classifier using a large training set. However a single classifier using a small training set may or may not outperform that with a large training set. The following experiments were performed to ascertain the optimum size of the training set. For the many neural networks produced by training using randomly chosen small data sets, an ROC plot from their averaged outputs was compiled after feeding the test data to each of them in turn. To find the optimum size of the training set, sizes of small training sets of melanomas

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plus moles were chosen at 3+3, 6+6, 9+9, 16+16, 23+23, 30+30, and tested together with the large training set of 36+36. In the experiments 15 training sets were randomly selected for each size from the full set of training data. Fig.9 presents the performance using the area under the ROC plot against training set size for the pre- and post-selection schemes. The trace marked by diamonds is for a ROC plot from the averaged outputs of the 15 classifiers before feature selection whereas that marked by circles is post feature selection. As indicated in Fig.9, the scheme using the averaged outputs of the 15 classifiers post-feature selection performs best. It was noticed from the experiments that the averaged output value of all

networks, using a combination model of many parallel network classifiers, may overcome the

weakness of any single classifiers in the case of small training sets. The peak area of the ROC for the averaged outputs of the neural network classifiers, post-feature selection was for a training set of 9 melanomas plus 9 moles, indicating this to be the optimum size.

Fig.9 Performance against size of training set

Table 2 lists the ROC performances for each of the two single scale and the four multi-scale schemes tested. The performance is indicated by the measures of the sensitivity, specialty and area covered by each ROC plot, where the paired values of sensitivity and specialty are the True Positive Rate (TPR) and False Positive Rate (FPR) coordinates of the point on each ROC plot closest to the top left corner [21,22,23]. With the lowest values, the single scale features with the small training set have the worst results, and the multi-scale features after feature selection and using the small training set the best.

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Scheme Specialty Sensitivity Area of ROC Single scale features with small sample set 0.64566 0.69444 0.69534 Single scale features with large sample set 0.87903 0.55556 0.75179 Original multi-scale features with small sample set 0.83871 0.69444 0.81541 Original multi-scale features with large sample set 0.80645 0.69444 0.81989 Selected multi-scale features with large sample set 0.74194 0.83333 0.83333 Selected multi-scale features with small sample set 0.90323 0.83333 0.89068

Table 2. Comparison of classification performances

5.3.4 Discussion In general, Fig.8 and Table 2 indicate that multi-scale features have better discrimination than single scale features, and that, after feature selection, multi-scale schemes have better performances than schemes without selection. The best ROC plot was for multi-scale selected features using the small training set. It outperformed the corresponding scheme using the large training set. There are two reasons for this in that each of the 13 selected multi-scale features had a good individual performance when used for skin contour irregularity measurement and so a small training set was probably sufficient. Secondly the performance of a neural network with a BP training algorithm can be degraded by using a large training set that may cause a solution to become stuck in a local minimum [24].

6 Conclusions A method that examines the structural content of the contour of skin lesion images has been proposed that determines if the lesion is a melanoma or a benign mole. The contour contained both structural and textural information, but it was demonstrated that the structural information was most important in the determination. The 1D contour signal was filtered into sub-bands using the discrete wavelet transform (DWT) down to level 9. The structural information was found to lie mostly at the lower frequencies, in the detail levels from 6 to 9 plus the approximation at level 9. These were denoted as significant levels, and the information within them was shown to provide the best classification separation between sets of melanomas and moles. The DWT was found to enable efficient processing of the signals. A number of statistical and geometric feature descriptors of contour irregularity were developed. These were computed in each of the significant sub-bands. To enable an efficient system, these features were selected using a two stage process. Firstly correlation analysis was used to remove redundant features, and secondly the performance of each feature in separating sets of melanomas and moles was measured and compared.

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A classifier using a combination of features was designed using a back-projection neural network. The system was optimized to obtain the maximum true positive rate and minimum false positive rate for separation. Issues of training were explored, and a small, randomly chosen, sub-set of 9 melanoma and 9 mole images found to provide the best results. Of the seven available features, six were applied in four significant sub-bands and one in a single sub-band, forming twenty five measurements in total. As described above these had been ranked in order of effectiveness, and it was found the best combined classifier resulted when just the best thirteen measures were used. Acknowledgement: This work is supported by National Scientific foundation of China (60775016). References [1] C. Grana, G. Pellacani, R. Cucchiara, S. Seidennari. A new algorithm for border description of polarized light surface microscopic images of pigmented skin lesions, IEEE Transactions on Medical Imaging 22 (8) (2003) 959-964. [2] C. Serrano, B. Acha, Pattern analysis of dermoscopic images based on Markov random fields, Pattern Recognition 42 (6) (2009) 1052-1057. [3] A. Chiem, A. Al-Jumaily, R. N. Khushaba, A Novel Hybrid System for Skin Lesion Detection, in: Proceedings of the 3rd International Conference on Intelligent Sensors, Sensor Networks and Information, ISSNIP, Melbourne, Australia, 2007, pp. 567-572. [4] R. Narasimha, H. Ouyang, A. Gray, S. W. McLaughlin, S. Subramaniam, Automatic joint classification and segmentation of whole cell 3D images, Pattern Recognition, 42 (6) (2009) 1067-1079. [5] M. E. Vestergaard, P. Macaskill, P. E. Holt, S. W. Menzies, Dermoscopy compared with naked eye examination for the diagnosis of primary melanoma: a meta-analysis of studies performed in a clinical setting, British Journal of Dermatology 159 (3) (2008) 669-676. [6] P. Wighton, T. K. Lee, H. Lui, D. I. McLean, M. S. Atkins, Generalizing common tasks in automated skin lesion diagnosis, IEEE Transactions on Information Technology in Biomedicine 15 (4) (2011) 622-629. [7] T. K. Lee, D. I. McLean, M. S. Atkins, Irregularity Index: A new border irregularity measure for cutaneous melanocytic lesions, Medical Image Analysis 7 (1) (2003) 47-64. [8] S. V. Patwardhan, A. P. Dhawan, P. A. Relue, Classification of melanoma using tree structured wavelet transforms, Computer Methods and Programs in Biomedicine 72 (3) (2003) 223 – 239. [9] K. M. Clawson, P. Morrow, B. Scotney, J. McKenner, O. Dolan, Analysis of pigmented skin lesion border irregularity using the harmonic wavelet transform, in: Proceedings of the 13th International Machine Vision and Image Processing Conference IMIVP’09, Dublin, Ireland,

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[24] W. Jin, Z. J. Li, L. S. Wei, H. Zhen, The improvements of BP neural network learning algorithm, in: Proceedings of the 5th International Conference on Signal Processing, volume 3, Beijing, China, 2000, pp. 1647-1649. About the Author Li Ma received the B. S. and PhD degrees in Electrical Engineering from Central South University, P. R. China, in 1976 and 1998 respectively. She is currently a professor at the College of Life Information Science & Instrument Engineering, Hangzhou Dianzi University, P. R. China. She has been an academic visitor to the College of Cardiff, University of Wales, U.K. during 1993-1994, and a senior visiting fellow at the University of Warwick in 2003. Her research interests include industrial and medical image processing, video based monitoring systems, and pattern recognition. About the Author Richard Staunton received the B.Sc. (honours) degree in electronic engineering from the City University, UK, in 1973, and the Ph.D. degree in engineering from the University of Warwick, UK, in 1992. He is currently an Associate Professor in the School of Engineering at The University of Warwick, UK. From 1973 to 1977 he worked for the aerospace industry and from 1977 to 1986 for the UK National Health Service, where he engaged in research and development of medical image processing systems. His current research interests include depth from defocus, industrial image processing, hexagonal sampling systems, and medical image processing.